Tamás Erdélyi (mathematician)
|Known for||Polynomials, Approximation|
|Influenced||G.G. Lorentz William Bassichis|
Tamás Erdélyi is a Hungarian-born mathematician working at Texas A&M University. His main areas of research are related to polynomials and their approximations, although he also works in other areas of applied mathematics.
Life, education and positions
Tamás Erdélyi was born on September 13, 1961, in Budapest, Hungary. From 1980 to 1985 he studied mathematics at the ELTE in Budapest, where he received his diploma. After graduation, he worked for two years as a research assistant at the Mathematics Institute of the Hungarian Academy of Sciences. He later pursued his graduate studies at the University of South Carolina (1987–88) and the Ohio State University (1988–89). He received his Ph.D. from the University of South Carolina in 1989. He was a postdoctoral fellow at the Ohio State University (1989–92), Dalhousie University (1992–93), Simon Fraser University (1993–95), and finally at the University of Copenhagen (1996–97). In 1995, he started to work at the Texas A&M University in College Station, Texas, where he is a professor of mathematics.
Erdelyi has published papers dealing with other important inequalities for exponential sums and linear combinations of shifted Gaussians. Early in the twenty-first century he proved two of Saffari's conjectures, the phase problem and the near orthogonality conjecture. In 2007, working with Borwein, Ferguson, and Lockhart, he settled Littlewood's Problem 22. He is an expert on ultraflat and flat sequences of unimodular polynomials, having published papers on the location of zeros for polynomials with constrained coefficients, and on orthogonal polynomials. He has also made significant contributions to the integer Chebyshev problem, worked with Harvey Friedman on recursion theory, and, together with Borwein, disproved a conjecture made by the Chudnovsky brothers.
Erdelyi's more recent work has focused on problems in the interface of harmonic analysis and number theory, and the Mahler measure of constrained polynomials. In 2013 he proved that the Mahler measure and the maximum norm of the Rudin-Shapiro polynomials on the unit circle have the same size. He contributed substantially to Chowla's cosine problem by proving Bourgain and Ruzsa type results for the maximum and minimum of Littlewood cosine polynomials. One of his Bernstein type inequalities for rational functions is now referred to as the Borwein–Erdelyi inequality. He is also known for establishing the full Müntz theorem with Borwein and Johnson, and has some partial results related to questions raised by Paul Erdős.